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Fachbereich 3 - Mathematik und Informatik: Stochastics and Dynamical Systems

Publications

Books

 
  1. Kesseb?hmer, Marc; Munday, Sara; Stratmann, Bernd.
    Infinite Ergodic Theory of Numbers.
    De Gruyter Textbook, 191 pages (2016).
    ISBN: 978-3-11-043942-7.
 

Editor:

 
  1. Preface: Thermodynamic formalism - Applications to geometry, number theory, and stochastics. Stochastics and Dynamics Vol. 21, No. 03, 2102001 (2021).
    M. Kesseb?hmer, S. Kombrink, Y. Pesin, T. Samuel and J. Schmeling.
    DOI: 10.1142/S0219493721020019
 
 
  1. Preface: Diffusion on fractals and non-linear dynamics. Discrete Contin. Dyn. Syst. Ser. S 10(2), 2017.
    K. Falk, T. J?ger, M. Kesseb?hmer, J. Rademacher and T. Samuel.
    DOI: 10.3934/dcdss.201702i
 

Published Articles

 
  1. Kesseb?hmer, Marc; Niemann, Aljoscha; Samuel, Tony; Weyer, Hendrik.
    Generalised  Kre?n—Feller operators and gap diffusions via transformations of measure spaces.
    To appear in: "From Classical Analysis to Analysis on Fractals. A Tribute to Robert Strichartz, Volume 2", Applied and Numerical Harmonic Analysis, Birkh?user, 2024. 
    arXiv: 1909.08832.
 
 
  1. Ke?eb?hmer, Marc; Niemannn, Aljoscha; Zhu, Sanguo
    Quantization dimensions of compactly supported probability measures via Rényi dimensions
    Trans. Amer. Math. Soc. 376 (2023), 4661-4678
    DOI: 10.1090/tran/8863. arXiv: 2205.15776.
 
 
  1. Ke?eb?hmer, Marc; Niemann, Aljoscha
    Approximation order of Kolmogorov diameters via Lq-spectra and applications to polyharmonic operators.
    Journal of Functional Analysis, Volume 282, Issue 9, 2022, Article 109598, ISSN 0022-1236
    DOI: 10.1016/j.jfa.2022.109598. arXiv: 2107.07932.
 
 
  1. Kesseb?hmer, Marc; Niemann, Aljoscha
    Spectral asymptotics of Kre?n-Feller operators for weak Gibbs measures on self-conformal fractals with overlaps
    Advances in Mathematics, Volume 403, 2022, Paper No. 108384, ISSN 0001-8708.
    DOI: 10.1016/j.aim.2022.108384. arXiv: 2107.02616.
 
 
  1. Kesseb?hmer, Marc; Niemann, Aljoscha.
    Spectral dimensions of Kre?n-Feller operators and Lq-spectra.
    Advances in Mathematics, Volume 399, 2022.
    DOI: 10.1016/j.aim.2022.108253. arXiv: 2106.08862.
 
 
  1. Gr?ger, Maik; Jaerisch, Johannes; Kesseb?hmer, Marc.
    Thermodynamic formalism for transient dynamics on the real line.
    Nonlinearity 35, 1093–1118  (2022).
    DOI: 10.1088/1361-6544/ac45ea. arXiv: 1905.09077.
 
 
  1. Jaerisch, Johannes; Kesseb?hmer, Marc; Munday, Sara.
    A multifractal analysis for cuspidal windings on hyperbolic surfaces.
    Stochastics and Dynamics Vol. 21, No. 03, 2140007 (2021).
    DOI: 10.1142/S0219493721400074. arXiv: 1610.05827.
 
 
  1. Kesseb?hmer, Marc; Schindler, Tanja.
    Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails.
    Nonlinearity 33(10): 5543?–5566 (2020).
    DOI: 10.1088/1361-6544/ab9585. arXiv: 1903.09337.
 
 
  1. Kesseb?hmer, Marc; Rademacher, Jens; Ulbrich, Dennis.
    Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata.
    Ergodic Theory and Dynamical Systems 41 (2020), no. 5, 1397–1430.
    DOI: 10.1017/etds.2020.18. arXiv: 1903.02459.
 
 
  1. Kesseb?hmer, Marc; Samuel, Tony; Weyer, Hendrik.
    Measure-geometric Laplacians for partially atomic measures.
    Comment. Math. Univ. Carolin. 61, 313-335 (2020).
    DOI: 10.14712/1213-7243.2020.026
    Title of preprint: Measure-geometric Laplacians on the real line. arXiv: 1802.04858.
 
 
  1. Kesseb?hmer, Marc; Schindler, Tanja.
    Limit theorems for counting large continued fraction digits.
    Lith Math J 60: 189–207 (2020). 
    DOI:10.1007/s10986-020-09479-5. arXiv: 1604.06612.
 
 
  1. Kesseb?hmer, Marc; Samuel, Tony; Sender, Karenina.
    The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain.
    J. Fractal Geom.7: 113–136 (2020).
    DOI: 10.4171/JFG/86. arXiv: 1710.04414.
 
 
  1. Kesseb?hmer, Marc; Schindler, Tanja.
    Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type.
    Dynamical Systems. An International Journal 35(2): 275-305 (2020).
    DOI: 10.1080/14689367.2019.1667305. arXiv: 1901.04478.
 
 
  1. Baake, Michael; Gohlke, Philipp; Kesseb?hmer, Marc; Schindler, Tanja.
    Scaling properties of the Thue--Morse measure.
    Discrete Contin. Dyn. Syst. Ser. A, 39(7): 4157?–4185 (2019).
    DOI: 10.3934/dcds.2019168. arXiv: 1810.06949.
 
 
  1. Kesseb?hmer, Marc; Mosbach, Arne; Samuel, Tony; Steffens, Malte.
    Diffraction of return time measures.
    J. Stat. Phys. 174(3): 519–535 (2019).
    DOI: 10.1007/s10955-018-2196-5. arXiv: 1801.07608.
 
 
  1. Kesseb?hmer, Marc; Schindler, Tanja.
    Strong laws of large number for intermediately trimmed Birkhoff sums of observables with infinite mean.
    Stochastic Processes and their Applications 129(10): 4163?–4207 (2019).
    DOI: 10.1016/j.spa.2018.11.015. arXiv: 1706.07369.
 
 
  1. Kesseb?hmer, Marc; Samuel, Tony; Weyer, Hendrik.
    Measure-geometric Laplacians for discrete distributions.
    In Niemeyer et al., editor, Horizons of Fractal Geometry and Complex Dimensions, volume 731 of Contemp. Math., pages 133–142. Amer. Math. Soc., Providence, R.I. (2019). 
    DOI: 10.1090/conm/731/14676. arXiv: 1702.03873.
 
 
  1. Dreher, Fabian; Kesseb?hmer, Marc.
    Escape rates for special flows and their higher order asymptotics.
    Ergod. Th. & Dynam. Sys. 39(6): 1501–1530 (2019).
    DOI: 10.1017/etds.2017.76. arXiv: 1605.00467.
 
 
  1. Kesseb?hmer, Marc; Schindler, Tanja.
    Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite mean.
    J.Theor. Probab., 32(2): 702–720 (2019).
    DOI: 10.1007/s10959-017-0802-0. arXiv: 1609.04910.
 
 
  1. Gr?ger, Maik; Kesseb?hmer, Marc; Mosbach, Arne; Samuel, Tony; Steffens, Malte.
    A classification of aperiodic order via spectral metrics and Jarník sets.
    Ergodic Theory and Dynamical Systems, 39(11): 3031?–3065 (2019).
    DOI: 10.1017/etds.2018.7 arXiv: 1601.06435.
 
 
  1. Dreher, Fabian; Kesseb?hmer, Marc; Mosbach, Arne; Samuel, Tony; Steffens, Malte.
    Regularity of aperiodic minimal subshifts.
    Bull. Math. Sci. 8(3): 413–434 (2018).
    DOI: 10.1007/s13373-017-0102-0. arXiv: 1610.03163.
 
 
  1. Fuhrmann, Gabriel; Gr?ger, Maik; J?ger, Tobias.
    Non-smooth saddle-node bifurcations II: dimensions of strange attractors.
    Ergodic Theory Dynam. Systems 38(8): 2989?–3011(2018).
    DOI: 10.1017/etds.2017.4. arXiv: 1412.6054.
 
 
  1. Kesseb?hmer, Marc; Kombrink, Sabrina.
    A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory.
    Discrete Contin. Dyn. Syst. -- Ser. S 2(10): 335–352 (2017).  
    DOI: 10.3934/dcdss.2017016. arXiv: 1604.08252.
 
 
  1. Kesseb?hmer, Marc; Zhu, Sanguo.
    The upper and lower quantization coefficient for Markov-type measures.
    Mathematische Nachrichten 290(5-6): 827–839 (2017).
    DOI: 10.1002/mana.201500328.
    Title of preprint: The quantization for Markov-type measures on a class of ratio-specified graph directed fractals. arXiv:1406.3257.
 
 
  1. Gr?ger, Maik; J?ger, Tobias.
    Some remarks on modified power entropy.
    Dynamics and Numbers, Contemp. Math. 669: 105–122 (2016).
    DOI: 10.1090/conm/669/13425. arXiv: 1506.07192.
 
 
  1. Fuhrmann, Gabriel; Gr?ger, Maik; J?ger, Tobias.
    Amorphic complexity.
    Nonlinearity 29(2): 528–565 (2016).
    DOI: 10.1088/0951-7715/29/2/528. arXiv: 1503.01036.
 
 
  1. Das, Tushar; Stratmann, Bernd O.; Urbánski, Mariusz.
    Geometry of limit sets of discrete groups acting on real infinite-dimensional hyperbolic space.
    Stochastics and Dynamics 16(5), 17 pages (2016).
    DOI: 10.1142/S0219493716500180.
 
 
  1. Kesseb?hmer, Marc; Samuel, Tony; Weyer, Hendrik.
    A note on measure-geometric Laplacians. 
    Monatsh. Math. 181(3): 643–655 (2016).
    DOI: 10.1007/s00605-016-0906-0. arXiv: 1411.2491.
 
 
  1. Kautzsch, Johannes; Kesseb?hmer, Marc; Samuel, Tony.
    On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps.
    Ann. Henri Poincaré 17(9): 2585?–2621 (2016).
    DOI:10.1007/s00023-015-0451-8. arXiv: 1410.3805.
 
 
  1. Kesseb?hmer, Marc; Zhu, Sanguo.
    On the quantization for self-affine measures on Bedford-McMullen carpets.
    Mathematische Zeitschrift 283(1): 39–58 (2016).
    DOI: 10.1007/s00209-015-1588-3. arXiv: 1312.3289.
 
 
  1. Li, Bing; Sahlsten, Tuomas; Samuel, Tony.
    Intermediate β-shifts of finite type.
    Discrete Contin. Dyn. Syst. 36(1): 323–344 (2016).
    DOI: 10.3934/dcds.2016.36.323. arXiv: 1401.7027.
 
 
  1. Kesseb?hmer, Marc; Zhu, Sanguo.
    Some recent developments in quantization of fractal measures.
    Fractal geometry and stochastics V, Progr. Probab. 70: 105–120 (2015).
    DOI: 10.1007/978-3-319-18660-3_7. arXiv: 1501.04814.
 
 
  1. Kautzsch, Johannes; Kesseb?hmer, Marc; Samuel, Tony; Stratmann, Bernd O.
    On the asymptotics of the α-Farey transfer operator.
    Nonlinearity 28: 143–166 (2015). 
    DOI: 10.1088/0951-7751/28/1/143. arXiv: 1404.5857.
 
 
  1. Kesseb?hmer, Marc; Kombrink, Sabrina.
    Minkowski content and fractal Euler characteristic for conformal graph directed systems.
    Journal of Fractal Geometry 2: 171–227  (2015). 
    DOI: 10.4171/JFG/19. arXiv: 1211.733
 
 
  1. Falk, Kurt; Matsuzaki, Katsuhiko.
    The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group.
    Conf. Geom. Dyn. 19: 159–196 (2015).
    DOI: 10.1090/ecgd/279. arXiv: 1106.4409.
 
 
  1. Dreher, Fabian; Samuel, Tony.
    Continuous images of Cantor's ternary set.
    Amer. Math. Monthly 121(7): 640–643 (2014).
    DOI: 10.4169/amer.math.monthly.121.07.640. arXiv: 1303.3810.
 
 
  1. Samuel, Tony; Snigireva, Nina; Vince, Andrew.
    Embedding the symbolic dynamics of Lorenz maps.
    Math. Proc. Camb. Phil. Soc. 156(3): 505–519 (2014).
    DOI: 10.1017/S0305004114000061. arXiv: 1205.1197.
 
 
  1. Jaerisch, Johannes; Kesseb?hmer, Marc, Lamei, Sanaz.
    Induced topological pressure for countable state Markov shifts.
    Stoch. Dyn. 14(2), 31 pages (2014).
    DOI: 10.1142/S0219493713500160. arXiv: 1010.2162.
 
 
  1. Buckley, Stephen M.; Falk, Kurt.
    The boundary at infinity of a rough CAT(0) space. 
    Anal. Geom. Metric Spaces 2: 53–80 (2014).
    DOI: 10.2478/agms-2014-0002. arXiv: 1209.6557.
 
 
  1. Mihailescu, Eugen; Stratmann, Bernd O.
    Upper estimates for stable dimensions of fractal sets with variable numbers of foldings.
    International Mathematics Research Notices, rnt168, 23 pages (2013). 
    DOI:10.1093/imrn/rnt168. arXiv: 1301.1827.
 
 
  1. Gr?ger, Maik; J?ger, Tobias.
    Dimensions of attractors in pinched skew products.
    Comm. Math. Phys. 320(1): 101–119 (2013). 
    DOI: 10.1007/s00220-013-1713-2. arXiv: 1111.6574. 
 
 
  1. Gr?ger, Maik; Hunt, Brian R.
    Coupled skinny baker's maps and the Kaplan-Yorke conjecture.
    Nonlinearity 26(9): 2641?–2667 (2013). 
    DOI: 10.1088/0951-7715/26/9/2641. arXiv: 1303.0030.
 
 
  1. Buckley, Stephen M.; Falk, Kurt.
    Natural maps between CAT(0) boundaries.
    New York J. Math. 19: 13–22 (2013).
    arXiv: 1210.4812. 
 
 
  1. Jaerisch, Johannes; Kesseb?hmer, Marc; Stratmann, Bernd O.
    A Fréchet law and an Erd?s-Philipp law for maximal cuspidal windings.
    Ergodic Theory Dynam. Systems 33(4): 1008–1028 (2013).
    DOI:10.1017/S0143385712000235. arXiv: 1109.3583.
 
 
  1. Samuel, Tony.
    A simple proof of Vitali's theorem for signed measures.
    Amer. Math. Monthly 120(7): 654–660 (2013).
    DOI: 10.4169/amer.math.monthly.120.07.654. arXiv: 1202.2106.
 
 
  1. Kesseb?hmer, Marc; Samuel, Tony.
    Spectral metric spaces for Gibbs measures.
    J. Funct. Anal. 31: 1801–1828 (2013).
    DOI: 10.1016/j.jfa.2013.07.012. arXiv: 1012.5152.
 
 
  1. Buckley, S. M.; Falk, K.
    Rough CAT(0) spaces.
    Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103), no. 1: 3–33 (2012).
    arXiv: 1104.1947.
 
 
  1. Bohnstengel, Jana; Kesseb?hmer, Marc.
    Multiresolution analysis for Markov Interval Maps.
    Numer. Funct. Anal. and Optim. 33(7-9): 791–832 (2012). 
    DOI: 10.1080/01630563.2012.682126. arXiv: 1107.0275.
 
 
  1. Freiberg, Uta; Kombrink, Sabrina.
    Minkowski content and local Minkowski content for a class of self-conformal sets.
    Geom. Dedicata 159(1): 307–325 (2012).
    DOI:10.1007/s10711-011-9661-5. arXiv: 1109.3896.
 
 
  1. Kesseb?hmer, Marc; Kombrink, Sabrina.
    Fractal curvature measures and Minkowski content for self-conformal subsets of the real line.
    Adv. in Math. 230: 2474?–2512 (2012). 
    DOI: 10.1016/j.aim.2012.04.023.
    Title of preprint: Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets. arXiv: 1012.5399.
 
 
  1. Kesseb?hmer, Marc; Stratmann, Bernd.
    A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence.
    Unif. Distrib. Theory 7(2): 21–33 (2012).
    arXiv: 1009.1823.
 
 
  1. Kesseb?hmer, Marc; Munday, Sara; Stratmann, Bernd O.
    Strong renewal theorems and Lyapunov spectra for α-Farey and α-Lüroth systems.
    Ergod. Theory Dyn. Syst. 32(3): 989?–1017 (2012).
    DOI: 10.1017/S0143385711000186. arXiv:1006.5693.
 
 
  1. Denker, Manfred; Stratmann, Bernd O.
    The Patterson measure: classics, variations and applications.
    Contributions to Analytic and Algebraic Number Theory - Festschrift for S. J. Patterson, Series: Springer Proceedings in Mathematics, Vol. 9, Blomer, Valentin; Mih?ilescu, Preda (Eds.)  (2012), 171-195. 
    DOI: 10.1007/978-1-4614-1219-9_7.  
 
 
  1. Kesseb?hmer, Marc; Stratmann, Bernd O.
    A note on the algebraic growth rate of Poincaré series for Kleinian groups.
    Contributions in analytic and algebraic number theory, Springer Proc. Math., 9, Springer, New York, (2012),  237–245. 
    DOI: 10.1007/978-1-4614-1219-9_10. arXiv: 0910.5560.
 
 
  1. Kesseb?hmer, Marc; Stratmann, Bernd O.
    On the asymptotic behaviour of the Lebesgue measure of sum-level sets for continued fractions.
    Discrete Contin. Dyn. Syst. 32(7): 2437?–2451 (2012).
    DOI: 10.3934/dcds.2012.32.2437.
    Title of preprint: On the Lebesgue measure of sum-level sets for continued fractions. arXiv: 0901.1787.
 
 
  1. Falconer, Kenneth; Samuel, Tony.
    Dixmier traces and coarse multifractal analysis.
    Ergod. Theory Dyn. Syst. 31: 369–381 (2011).
    DOI:  10.1017/S0143385709001102. arXiv: 0905.3052.
 
 
  1. Bohnstengel, Jana; Jorgensen, Palle.
    Geometry of spectral pairs.
    Anal. Math. Phys. 1(1): 69–99 (2011). 
    DOI: 10.1007/s13324-011-0005-2.
 
 
  1. Jaerisch, Johannes; Kesseb?hmer, Marc.
    Regularity of multifractal spectra of conformal iterated function systems.
    Trans. Amer. Math. Soc. 363(1): 313–330 (2011).
    DOI: 10.1090/S0002-9947-2010-05326-7. arXiv: 0902.2473.
 
 
  1. Falk, Kurt; Matsuzaki, Katsuhiko; Stratmann, Bernd O.
    Checking atomicity of conformal ending measures for Kleinian groups.
    Conform. Geom. Dyn. 14: 167–183 (2010).
    DOI: 10.1090/S1088-4173-2010-00209-2. arXiv: 0903.3332.
 
 
  1. Bohnstengel, Jana; Kesseb?hmer, Marc.
    Wavelets for iterated function systems.
    J. Funct. Anal. 259(3): 583–601 (2010).  
    DOI: 10.1016/j.jfa.2010.04.014.
 
 
  1. Jaerisch, Johannes; Kesseb?hmer, Marc.
    The arithmetic-geometric scaling spectrum for continued fractions.
    Ark. Mat. 48(2): 335–360 (2010).  
    DOI: 10.1007/s11512-009-0102-8. arXiv: 0808.2308.
 
 
  1. Buckley, Stephen M.; Falk, Kurt H.; Wraith, David J.
    Ptolemaic spaces and CAT(0).
    Glasgow Math. J. 51: 301–314 (2009). 
    DOI: 10.1017/S0017089509004984. 
 
 
  1. Schmeling, J?rg; Stratmann, Bernd O.
    The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics.
    Kodai Math. J. 32(2): 179–196 (2009).
    DOI: 10.2996/kmj/1245982902. arXiv: 0801.3962.
 
 
  1. Jordan, Thomas; Kesseb?hmer, Marc; Pollicott, Mark; Stratmann, Bernd O.
    Sets of nondifferentiability for conjugacies between expanding interval maps.
    Fund. Math. 206: 161–183 (2009).
    DOI: 10.4064/fm206-0-10. arXiv: 0807.0115.
 
 
  1. Kesseb?hmer, Marc; Stratmann, Bernd O.
    H?lder-differentiability of Gibbs distribution functions.
    Math. Proc. Cambridge Philos. Soc. 147(2): 489–503 (2009).
    DOI: 10.1017/S0305004109002473. arXiv: 0711.4698.
 
 
  1. Kesseb?hmer, Marc; Stratmann, Bernd O.
    Fractal analysis for sets of non-differentiability of Minkowski's question mark function.
    J. Number Theory 128(9): 2663?–2686 (2008).
    DOI: 10.1016/j.jnt.2007.12.010. arXiv: 0706.0453.
 
 
  1. Kesseb?hmer, Marc; Slassi, Mehdi.
    Large deviation asymptotics for continued fraction expansions.
    Stoch. Dyn. 8(1): 103–113 (2008).
    DOI: 10.1142/S0219493708002226. arXiv: 0702381.
 
 
  1. Bonfert-Taylor, Petra; Falk, Kurt; Taylor, Edward C.
    Gaps in the exponent spectrum of subgroups of discrete quasiconformal groups.
    Kodai Math. J. 31(1): 68–81 (2008).
    DOI: 10.2996/kmj/1206454552.
 
 
  1. Kesseb?hmer, Marc; Stratmann, Bernd O.
    Refined measurable rigidity and flexibility for conformal iterated function systems.
    New York J. Math. 14: 33–51 (2008).
    arXiv: 0603571.
 
 
  1. Kesseb?hmer, Marc; Slassi, Mehdi.
    A distributional limit law for the continued fraction digit sum.
    Math. Nachr. 281(9): 1294–1306  (2008).
    DOI: 10.1002/mana.200510679. arXiv: 0509559.
 
 
  1. Kesseb?hmer, Marc; Urbański, Mariusz.
    Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems.
    Nonlinearity 20(8): 1969–1985 (2007).
    DOI: 10.1088/0951-7715/20/8/009. arXiv: 0701541.
 
 
  1. Kesseb?hmer, M.; Stratmann, B. O.
    Homology at infinity; fractal geometry of limiting symbols for modular subgroups.
    Topology 46(5): 469–491 (2007).
    DOI: 10.1016/j.top.2007.03.004.
    Title of preprint: Limiting modular symbols and their fractal geometry. arXiv: 0611048.
 
 
  1. Kesseb?hmer, Marc; Slassi, Mehdi.
    Limit laws for distorted critical return time processes in infinite ergodic theory.
    Stoch. Dyn. 7(1): 103–121 (2007).
    DOI: 10.1142/S0219493707001962.
    Title of preprint: Critical waiting time processes in infinite ergodic theory. arXiv: 0607681.
 
 
  1. Kesseb?hmer, Marc; Stadlbauer, Manuel; Stratmann, Bernd O.
    Lyapunov spectra for KMS states on Cuntz-Krieger algebras.
    Math. Z. 256(4): 871–893 (2007).
    DOI: 10.1007/s00209-007-0110-y.
    Title of preprint: Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states. arXiv: 0601354.
 
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